An improved genetic algorithm for multi-floor facility layout problems having inner structure walls and passages

Abstract

This study proposes an improved genetic algorithm to derive solutions for multi-floor facility layouts that are to have inner structure walls and passages. The proposed algorithm models the multi-floor layout of facilities on gene structures. These gene structures consist of a five-segmented chromosome. Improved solutions are produced by employing genetic operations known as selection, crossover, inversion, mutation, and refinement of these genes for successive generations. All relationships between the facilities, passages, and lifts are represented as an adjacency graph. The shortest path and distance between two facilities is calculated using Dijkstra's algorithm of the graph theory. Comparative testing shows that the proposed algorithm performs better than other existing algorithm for the multi-floor facility layout design. Finally, the proposed algorithm is applied to the multi-deck compartment layout problem of the ship with the computational result compared with the multi-deck compartment layout of the actual ship.

Introduction

Facility layout problems (FLPs) concerning space layout optimization have been investigated in depth by researchers in many engineering fields. Recent advances in computing science and increased understanding of methods for developing mathematical models have helped with layout design investigations. The FLP has applications in both manufacturing and the service industry now. The FLP is a common industrial problem of allocating facilities to minimize the total cost of transporting materials [2] or to maximize adjacency requirement [3] or to both minimize the cost of transporting materials and maximize adjacency requirement between the facilities [4].

The FLP can be classified in two categories according to the arrangement method of facilities; either an equal area layout problem or an unequal area layout problem. The unequal area layout problem can be classified primarily into two categories depending on the plan type that the facility layout is to be drawn; either a grid-based block plan layout problem or a continual block plan layout problem. In the grid-based block plan layout problem the facility layout is constructed on the grid plan, called the grid-based block plan and divided into squares or rectangles having a unit area. In continual block plan layout problem the facility layout is constructed on the continual plan. To solve grid-based block plan layout problems which have a single-floor, various algorithms such as CRAFT [5], ALDEP [6], CORELAP [7], FRAT [8], COFAD [9], FLAC [10], DISCON [11], and SHAPE [12] have been developed by several researchers. Tam and Li [13], van Camp et al. [14], Tam [15], [16], Lacksonen [17], Tate and Smith [18], and Meller et al. [19] developed algorithms to solve the continual block plan layout problems. Graph theoretic algorithms have also been developed for solving the unequal area layout problem [20], [21].

The FLP can be classified in two categories according to the number of floors that facilities are allocated; either a single-floor facility layout problem or a multiple-floor facility layout problem [22]. Most algorithms for the FLPs were developed to solve the single-floor facility layout problems in the past and various algorithms have been recently developed to solve the multi-floor facility layout problems such as SPACECRAFT [23], MULTIPLE [24], SABLE [25], STAGES [26], etc.

However, the algorithms mentioned above for the unequal area layout problem cannot consider inner structure walls and passages in the available area. They are also limited to a rectangular boundary shape of the block plan. Therefore, these algorithms could not be directly applied to problems such as ship compartment layout problems. We proposed an algorithm which can be applied to the FLPs having the inner structure walls and passages, and the available area of the curved boundary shape, one year ago as previous research [1]. The previous algorithm by us could be successfully applied to FLPs of the ship, referred to as ship compartment layout problems. However, the algorithm could treat only single-floor facility layout problems, and did not consider adjacency relationship between facilities. To be applied to multi-floor facility layout problems such as multi-deck compartment layout problems of the actual ship, the previous algorithm by us is needed to be expanded.

In this study, an improved genetic algorithm is proposed for solving multi-floor facility layout problems having the inner structure walls and passages within available areas of the curved boundary by extending our previous work [1]. Comparative testing shows that the proposed algorithm performs better than other algorithm for the multi-floor facility layout design. Finally, the proposed algorithm is applied to multi-deck compartment layout problem of the ship having inner structure walls and passages, with a computational result compared with the multi-deck compartment layout of the actual ship.